MarkovModel
abstract class MarkovModel<Parameter, State> < Model
Markov model.
classDiagram
Model <|-- MarkovModel
MarkovModel <|-- HiddenMarkovModel
HiddenMarkovModel -- StateSpaceModel
link Model "../Model/"
link MarkovModel "../MarkovModel/"
link HiddenMarkovModel "../HiddenMarkovModel/"
link StateSpaceModel "../StateSpaceModel/"
The joint distribution is:
\underbrace{p(\mathrm{d}\theta, \mathrm{d}x_{1:T})}_{\text{joint}} =
\underbrace{p(\mathrm{d}\theta)}_{\text{parameter}}
\underbrace{p(\mathrm{d}x_1 \mid \theta)}_{\text{initial}}
\prod_{t=2}^T
\underbrace{p(\mathrm{d}x_t \mid x_{t-1}, \theta)}_{\text{transition}}.
A model derived from MarkovModel overrides the parameter(),
initial() and transition() member functions to specify the individual
components of the joint distribution. The MarkovModel class itself
overrides the simulate() and simulate(t) member functions of
Model to call these more specific functions internally.
Member Variables
| Name | Description |
|---|---|
| θ:Parameter | Parameter. |
| x:Tape<State> | States. |
Member Functions
| Name | Description |
|---|---|
| parameter | Parameter model. |
| initial | Initial model. |
| transition | Transition model. |
Member Function Details
initial
function initial(x:State, θ:Parameter)
Initial model.
- x: The initial state, to be set.
- θ: The parameters.
parameter
function parameter(θ:Parameter)
Parameter model.
- θ: The parameters, to be set.
transition
function transition(x:State, u:State, θ:Parameter)
Transition model.
- x: The current state, to be set.
- u: The previous state.
- θ: The parameters.